This invention relates to a method for interferometric measurement, which method comprises emitting waves onto a reference surface and onto a measured object which each reflect a part of the emitted waves, and receiving both the reflected parts of the waves by one and the same receiver, in which a representation of the measured object is generated from the reflected parts of the waves in the form of an interferogram, from which the form of the measured object is determined.
In addition to the method this invention also relates to an apparatus for interferometric measurement which includes a light source for emitting light, a reference surface for reflecting a first part of said light and a receiver which is arranged to receive the first part of the light and a second part of the light, reflected by an object, a representation of the measured object being generated in said receiver in the form of an interferogram from which the form of the measured object is determinable.
Optical interferometry is often used for non-contact measurement of the form of surfaces. For this purpose light which has been separated into two parts by the use of a prism, a semitransparent mirror or some other device is employed. One of these parts of the light illuminates and is reflected by a plane reference surface. The other part of the light illuminates and is reflected by the surface, the form of which is to be measured. The two reflected parts of the light are brought together to illuminate photographic film or some form of light recording electronics. The image thus produced is called an interferogram. From the interferogram the form of the surface can be determined. One example of an apparatus for Producing interferograms is shown schematically in FIG. 1.
In those cases where the light employed is monochromatic, i.e. all the light is of one and the same wavelength, the interferogram consists of light and dark regions. The lightest regions are generated where the two reflected parts of the light interfere constructively, i.e. where they are in phase. This is the case when the total distance (from the light source to the recording medium) is the same for the two parts of the light or when it differs by a whole number of wavelengths. The darkest regions are generated where the two reflected parts of the light interfere destructively, i.e. where they are in opposite phase. This is the case when the total distance (from the light source to the recording medium) for the two parts of the light differs by half a wavelength in addition to a whole number of wavelengths.
In those cases where the light employed is white, i.e. when the light is composed of light of different wavelengths, the interferogram consists of differently coloured regions. Light of one wavelength in the two reflected light components may interfere constructively in the same point where light of a different wavelength interferes destructively. In this way the spectral composition of the reflected light changes, i.e. the reflected light has a hue (dominant wavelength) as opposed to the case for the light source employed.
By analysing the changes in the interferogram, in intensity in monochromatic interferograms, in hue and possibly also intensity and saturation in interferograms recorded with white light sources, the position and form of the surface can be determined, although not always unambiguously.
When a monochromatic light source is employed, the surface can be translated in steps of half wavelengths (i.e. the total distance the light travels changes in steps of whole wavelengths) without changes in the interferogram. The determination of the position of the surface thus is ambiguous. Besides there is an ambiguity in the determination of the form of the surfacexe2x80x94an indentation in the surface may result in the same interferogram as a protuberance in the surface.
By employing a light source which emits white light, these ambiguities can be eliminated. However, the interval within which the form and position of the surface can be determined becomes very small, in the order of microns. Outside of this narrow interval so many interferences occur, both constructive and destructive, that the interferogram cannot be interpreted due to low colour saturation. In order to determine the position and form of a surface unambiguously, it is necessary to calibrate the instrumentation with the aid of a surface in an accurately known position and having an accurately known form (e.g. a spherical ball with known diameter, fastened in a fixed jig).
There are a number of important technical applications for measuring position and form within a very narrow interval. With a monochromatic light source it is then possible to eliminate ambiguities in the determination of the form of the surface by recording several (at least three) interferograms of the same surface with different displacements of the two light parts (e.g. a semitransparent mirror can be moved, see FIG. 2). This is called phase-stepping interferometry.
There are two kinds of phase-stepping interferometry. In the one kind, temporal phase-stepping, the interferograms are generated consecutively in time and it is thus assumed that the position and form of the surface is not changed during the time required to record all the necessary interferograms. In the other kind, usually called spatial phase-stepping, the different interferograms are generated simultaneously. This can be arranged in several different ways, e.g. by employing light with different polarisation angles. The instrumentation then is more extensive (e.g., three cameras must be used instead of one) but the form of the surface may change, which is necessary in many important applications.
In each of the references EP-A-506 296, EP-A-0 506 297 and the paper xe2x80x9cThree-color laser-diode interferometerxe2x80x9d, published in the journal Applied Optics, Vol. 30, No. 25, 1991, a method of extending the measurement range within which the structure of an object can be unambiguously determined is presented. This method is based on the employment of so-called synthetic wavelengths. Two monochromatic light rays with closely spaced wavelengths xcex1, xcex2, are generated by a laser diode and are directed onto the measured object. These light rays cooperate to generate a light ray with a so-called synthetic wavelength xcex912xe2x88x921=xcex1xe2x88x921xe2x88x92xcex2xe2x88x921, which is much longer than the individual wavelengths xcex1, xcex2 and therefore allows an unambiguous determination of larger structures of the measured object. In practice, however, two separate interferograms are detected, one for each of the wavelengths xcex1 and xcex2, from which information about the structure of the measured object can be extracted. These two interferograms are detected through temporal phase-stepping, and thus this method exhibits the aforementioned disadvantages. The two wavelengths xcex1 and xcex2 also must be very closely spaced, typically within 0.5 nm, and therefore the differences between the two measured interferograms are small which results in poor measurement accuracy. In practice therefore, in order to obtain an enhanced analysis of the structure of the measured object, one or several additional synthetic wavelengths, generated by combinations of light rays of different wavelengths and shorter than the first synthetic wavelength xcex912 are employed. The choice of synthetic wavelengths is determined by the wavelengths which are available from laser diodes of multimode type.
Against this background the object of the present invention is to overcome the disadvantages associated with the known technology and particularly with both the known phase-stepping solutions, since these solutions are otherwise very advantageous.
In accordance with the invention, this object is achieved by a method as described in the introduction by the emitted waves comprising waves of three well-defined wavelengths xcexd1, xcexd2 and xcexd3, where xcexd1xe2x89xa0xcexd2xe2x89xa0xcexd3, which wavelengths are chosen so that they substantially satisfy the mutual relation
xcexd1=(xcexd2xc2x7xcexd3)/(2xc2x7xcexd3xe2x88x92xcexd2)
and generate an interferogram each in the receiver.
In accordance with the method, phase-stepping is thus achieved by the emitted waves comprising waves the wavelengths of which are all different but adapted to each other. Since it is possible to generate these three wavelengths by simpler means than e.g. the aforementioned light with different polarisation angles and since the mutual relation is considerably simpler to handle, and additionally generates simultaneous interferograms, it is realised that the method in accordance with the invention overcomes the problems heretofore associated with phase-stepping. It is also realised that the invention is well applicable to other kinds of waves than the optic waves normally associated with phase-stepping. Finally it is realised that corresponding expressions for any of the other wavelengths, expressed in the two remaining wavelengths, can be given.
By well-defined wavelength for each one of the waves mentioned it is understood that the ratio between the spectral width (xcex94xcexd) and the mean wavelength (xcexd) for each wave is much smaller than 1. If one or several of the waves employed have too large spectral width compared to their mean wavelength, the corresponding interferogram will exhibit such large disturbances that the resulting measurement accuracy will be insufficient.
In accordance with the method of the invention, three interferograms (E1, E2, E3) are detected simultaneously. These three interferograms can mathematically be expressed as:   {                                          E            1                    =                      A            +                          B              ⁢                              xe2x80x83                            ⁢              cos              ⁢                              xe2x80x83                            ⁢                              (                                                      β                    ⁢                                          xe2x80x83                                        ⁢                    d                                                        v                    1                                                  )                                                                                              E            2                    =                      A            +                          B              ⁢                              xe2x80x83                            ⁢              cos              ⁢                              xe2x80x83                            ⁢                              (                                                      β                    ⁢                                          xe2x80x83                                        ⁢                    d                                                        v                    2                                                  )                                                                                              E            3                    =                      A            +                          B              ⁢                              xe2x80x83                            ⁢              cos              ⁢                              xe2x80x83                            ⁢                              (                                                      β                    ⁢                                          xe2x80x83                                        ⁢                    d                                                        v                    3                                                  )                                                        
where A and B are arbitrary constants, xcex2 is known and depends on the refractive index, and d is the sought quantity. The three wavelengths (xcexd1, xcexd2, xcexd3) are chosen to satisfy the equations:   {                                          1                          v              1                                =                                    Φ              0                        -                          Δ              ⁢                              xe2x80x83                            ⁢              Φ                                                                                1                          v              2                                =                      Φ            0                                                                    1                          v              3                                =                                    Φ              0                        +                          Δ              ⁢                              xe2x80x83                            ⁢              Φ                                          
where "PHgr"0 and xcex94"PHgr" are arbitrary constants. The latter system of equations yields the interdependency xcexd1=(xcexd2xc2x7xcexd3)/(2xc2x7xcexd3xe2x88x92xcexd2) between the wavelengths. This particular choice of wavelengths is explained by the fact that by algebraic manipulation, linear combinations N and D in accordance with:
N=E1xe2x88x92E3=2B sin(xcex2d"PHgr"0)sin(xcex2dxcex94"PHgr")
D=2E2xe2x88x92E1xe2x88x92E3=2B cos(xcex2d"PHgr"0)(1xe2x88x92cos(xcex2dxcex94"PHgr"))
can be obtained.
The linear combinations N and D are quantities which can be measured from the simultaneously detected interferograms (E1, E2, E3), and in accordance with that stated above, xcex2, "PHgr"0 and xcex94"PHgr" are known quantities. From these linear combinations the equation:       tan    ⁢          xe2x80x83        ⁢          (              β        ⁢                  xe2x80x83                ⁢        d        ⁢                  xe2x80x83                ⁢                  Φ          0                    )        =            N      D        ⁢          xe2x80x83        ⁢    tan    ⁢          xe2x80x83        ⁢          (              β        ⁢                  xe2x80x83                ⁢        d        ⁢                  xe2x80x83                ⁢        Δ        ⁢                  xe2x80x83                ⁢        Φ        ⁢                  /                ⁢        2            )      
is obtained. This equation can be solved for the unknown quantity d with some suitable numerical method.
More concrete and applied to optical wavelengths, the receiver or the recording medium (colour film or colour video) in accordance with the invention thus simultaneously records three different interferograms, one for each wavelength. The difference in total distance travelled by the two parts of the light (the part of the light which is reflected by the reference surface and that part of the light which is reflected by the surface, the position and form of which is to be determined) expressed in number of wavelengths will then be different for different wavelengths and the phase displacement between the two components will therefore be different in the three different interferograms. Therefore a kind of phase-stepping interferomety has been achieved. The special relation between the different wavelengths which is required in accordance with the invention then makes it possible to determine the position and form of the surface from the three interferograms even when there are relatively large variations in the surface.
In the method according to the invention, either electromagnetic or mechanical waves are employed. The former are typically light waves in the visual spectrum and/or neighbouring intervals, i.e. the UV and IR intervals, since reliable sources and receivers for electro-magnetic waves in these intervals are available. According to a preferred embodiment, the light waves have the wavelengths xcexR, xcexG and xcexB, where R, G and B represent the hues red, green and blue since these hues are suited for receivers in the form of an ordinary photographic film or a video camera. The electromagnetic waves, however, can be in an arbitrary wavelength range, preferably in a range where reliable transmitters and receivers are available, such as the radio or X-ray range, if this is estimated to be advantageous on a specific measuring occasion.
Among mechanical waves in this context sound waves (acoustic waves) are the most important. The depth of penetration of these waves depends on their wavelength and they are particularly useful for non-transparent objects. In this context ultrasound waves are preferable since reliable transmitters and receivers are available.
Besides the method, the present invention relates to an apparatus of the type mentioned in the introduction, which is particularly intended for the application of the method when light is employed. In the apparatus in accordance with the invention, more particularly the light source is designed to simultaneously emit light of three well-defined wavelengths xcexd1, xcexd2 and xcexd3, where xcexd1xe2x89xa0xcexd2xe2x89xa0xcexd3, which wavelengths are chosen to substantially satisfy the mutual relation
xcexd1=(xcexd2xc2x7xcexd3)/(2xc2x7xcexd3xe2x88x92xcexd2)
and generate an interferogram each in the receiver.
A thus designed apparatus is very simple in its construction as compared to the aforementioned solutions for phase-stepping interferometry but still constitutes a well-functioning unit in practice.
This applies particularly if the light source comprises a lamp for emitting white light, a light splitter for splitting the light from the lamp into three parts and an interference filter for each such part, the interference filters being arranged to transmit light of one of the three well-defined wavelengths xcexd1, xcexd2 and xcexd3, one for each filter. In this embodiment, the invention thus makes it possible to determine the form of a surface also from interferograms which have been obtained by means of a light source emitting white light. The essential advantage of this is that no calibration, involving a known surface, is necessary. Besides the problem relating to colour saturation outside of a narrow interval is elimlnated and the form of the surface may therefore vary within a larger interval than before.